Full entry |
PDF
(0.3 MB)
Feedback

semilinear parabolic equation; functional differential equation; integrodifferential equation; integral equation fractional evolution equation; global existence; stability; variation of parameters

References:

[1] G. Butler, T. Rogers: **A generalization of a lemma of Bihari and applications to pointwise estimates for integral equations**. J. Math. Anal. and Appl. 33 No 1 (1971), 77–81. MR 0270089 | Zbl 0209.42503

[2] G. DaPrato, M. Iannelli: **Regularity of solutions of a class of linear integrodifferential equations in Banach spaces**. J. Integral Equations Appl. 8 (1985), 27–40. MR 0771750

[3] W. E. Fitzgibbon: **Semilinear functional differential equations in Banach space**. J. Diff. Eq. 29 (1978), 1–14. MR 0492663 | Zbl 0392.34041

[4] A. Friedman: **Partial Differential Equations**. Holt, Rinehart and Winston, New York, 1969. MR 0445088 | Zbl 0224.35002

[5] Y. Fujita: **Integrodifferential equation which interpolates the heat equation and the wave equation**. Osaka J. Math. 27 (1990), 309–321. MR 1066629 | Zbl 0796.45010

[6] H. Hattori, J. H. Lightbourne: **Global existence and blow up for a semilinear integral equation**. J. Integral Equations Appl. V2, No4 (1990), 529–546. MR 1094482

[7] D. Henry: **Geometric theory of semilinear parabolic equations**. Springer-Verlag, Berlin, Heidelberg, New York, 1981. MR 0610244 | Zbl 0456.35001

[8] H. Hoshino: **On the convergence properties of global solutions for some reaction-diffusion systems under Neumann boundary conditions**. Diff. and Int. Eq. V9 No4 (1996), 761–778. MR 1401436 | Zbl 0852.35023

[9] M. Kirane, N. Tatar: **Asymptotic stability and blow up for a fractional evolution equation**. submitted.

[10] M. Medved’: **A new approach to an analysis of Henry type integral inequalities and their Bihari type versions**. J. Math. Anal. and Appl. 214 (1997), 349–366. MR 1475574 | Zbl 0893.26006

[11] M. Medved’: **Singular integral inequalities and stability of semilinear parabolic equations**. Archivum Mathematicum (Brno) Tomus 24 (1998), 183–190. MR 1629697 | Zbl 0915.34057

[12] M. W. Michalski: **Derivatives of noninteger order and their applications**. ”Dissertationes Mathematicae”, Polska Akademia Nauk, Instytut Matematyczny, Warszawa 1993. MR 1247113 | Zbl 0880.26007

[13] M. Miklavčič: **Stability for semilinear equations with noninvertible linear operator**. Pacific J. Math. 1, 118 (1985), 199–214. MR 0783024

[14] S. M. Rankin: **Existence and asymptotic behavior of a functional differential equation in a Banach space**. J. Math. Anal. Appl. 88 (1982), 531–542. MR 0667076

[15] R. Redlinger: **On the asymptotic behavior of a semilinear functional differential equation in Banach space**. J. Math. Anal. Appl. 112 (1985), 371–377. MR 0813604 | Zbl 0598.34053

[16] C. Travis, G. Webb: **Existence and stability for partial functional differential equations**. Trans. Amer. Math. Soc. 200 (1974), 395–418. MR 0382808 | Zbl 0299.35085

[17] C. Travis, G. Webb: **Existence, stability and compacteness in the $\alpha $-norm for partial functional differential equations**. Trans. Amer. Math. Soc. 240 (1978), 129–143. MR 0499583